Typing “poetry” into a search engine will get you nowhere; or rather, it will get you everywhere, which is no use at all. Every angsty teenager should write poetry, of course, but only in a vanishingly small number of cases should anyone else ever read it. Herewith a short list of readable poetry on the web.
Dead white men; or, “classical” poetry:
Steve Spanoudis’ Poet’s Corner offers 7600 poems by 780 poets indexed by author, title and subject. Biographies of about 30 and photographs of about 120 poets (many of them somewhat obscure) are also available. They accept submissions, if you have a favourite poet you’d like to see included (but beware copyright restrictions!). The daily poetry break features a poem a day from the Poet’s Corner collection, with commentary by Bob Blair. I frequently disagree with Bob’s opinions, but he’s interesting.
Representative Poetry Online includes about 2,900 English poems by over 400 poets. It’s based on a 1912 textbook but includes hundreds of additional poems and poets as well as biographical data, commentaries and other features.
The estimable Project Bartleby offers a wonderful selection of verse anthologies and volumes. Special mention here to the best anthology of English poetry ever made, the 1919 Oxford Book of English Verse. Quoth Q:

My wish is that the reader should in his own pleasure quite forget the editor